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Using Rolling Windows to Examine Volatility and Correlation Changes

Article Quant Q&A · Author: JMK
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Summary

The discussion considers how to examine whether emerging markets change in volatility and in correlation with developed-market indices. Rather than prescribing a split into halves or thirds, one answer recommends plotting rolling estimates to locate periods of interest. Its example calculates return volatility over a trailing one-month window, illustrating how a sliding standard deviation can show changing risk through time. Because the window uses past observations through the current date, the displayed volatility may lag sharp moves in daily returns; centered windows are possible but described as less common.

For formal testing of variance changes, another answer points to nonparametric methods used in academic research, while cautioning that their suitability depends on the research objective and that they have drawbacks. The excerpt does not provide a specific test, correlation-estimation procedure, data requirements, or guidance on choosing window lengths. Rolling plots are therefore an exploratory diagnostic rather than a complete statistical test of market integration or structural change.

Key ideas

  • A rolling window can help identify when volatility or correlation estimates appear to change.
  • A trailing volatility window uses past observations through the current date and can lag sudden return moves.
  • Nonparametric tests are one possible approach to testing variance changes, but their usefulness depends on the objective.
  • The discussion does not settle whether halves or thirds are preferable or specify a formal test for changing correlation.

Tags

VolatilityStatisticsEquities
Full text
# comparing volatility and correlation over time


# comparing volatility and correlation over time












I'm trying to figure out if some emerging markets change over time.

- First of all I am going to check for changes in volatility. What would be a good method to do this. And do you suggest comparing the first half of the time series with the second or comparing the first 1/3 with the last 1/3.

- Secondly, for the correlation. I would like to check if the correlation between one emerging market and the SPX or FTSE100 changes over time, because the correlation should increase as the market 'emerges' and integrates with the emerged markets. Here as well, I wonder whether I should use halves or thirds.

I'm trying to figure out what would be a good method to test this. Do you have any suggestions?

## Answer by Sergei Rodionov (score 1)

https://quant.stackexchange.com/a/61520

This depends on your objectives, but for a cursory examination look at the changes of volatility and correlation over time as suggested by @SachaTheBrave. The rolling (or sliding) window is quite helpful in locating the intervals of particular interest.

Here's an example which shows 1-day returns for three ETFs (SPY, EEM, and EWZ) and a 1-month sliding standard deviation of the returns:

```
SELECT symbol, time, daily_return, stddev(daily_return) as volatility 
FROM (
  SELECT symbol, time, close, close/LAG(close)-1 AS daily_return
  FROM atsd_session_summary 
  WHERE symbol = 'SPY.US'
  AND datetime BETWEEN '2020-01-01' AND current_day
)
WITH ROW_NUMBER(symbol ORDER BY time) BETWEEN 1 MONTH PRECEDING AND CURRENT ROW
```

This type of sliding window (preceding-to-current) is not centered, with the volatility visually lagging the deviations observed in the 1-day return series. Centered windows are possible but used less often.

## Answer by user42108 (score 0)

https://quant.stackexchange.com/a/58476

"First of all I am going to check for changes in volatility. What would be a good method to do this"

As mentioned in a response to a different question, there are a number of academic papers that use non-parametric tests for determining changes in variance/volatility in financial time series. Whether or not these are "good methods" depends on how you define "good" as they have some obvious drawbacks.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.